Collision detection using a multiple symbol noncoherent soft output detector

ABSTRACT

Systems and methods for detecting collisions in radio frequency tags in accordance with embodiments of the invention are disclosed. In one embodiment, a receiver system includes a receiver configured to receive and sample a phase modulated input signal, and a multiple symbol noncoherent soft output detector configured to receive the sampled input signal and to generate a soft metric indicative of the reliability of a detected symbol based upon observations over multiple symbols, a collision detector configured to calculate a decision metric from a set of soft metrics generated by the multiple symbol noncoherent soft output detector and detect a collision when the decision metric satisfies a predetermined criterion.

CROSS-REFERENCE TO RELATED APPLICATION

The present invention claims priority under 35 U.S.C. §119(e) to U.S.Provisional Patent Application Ser. No. 61/449,869 entitled “LLR forSymbol Stream Combining of FM0 with Preamble and Pilot”, filed Mar. 7,2011 and under 35 U.S.C. §120 as a Continuation-In-Part of U.S. patentapplication Ser. No. 13/414,616 entitled “Multiple Symbol NoncoherentSoft Output Detector,” to Dariush Divsalar filed Mar. 7, 2012, thedisclosures of which are incorporated by reference herein in itsentirety.

FIELD OF THE INVENTION

The present invention relates to communication systems and morespecifically to detection of tag collisions using a multiple symbolnoncoherent soft output detector.

BACKGROUND

In many applications, noncoherent or differential detection is anattractive alternative to coherent detection due to the simplicity ofimplementation and/or where the transmission environment is sufficientlydegraded, e.g., a multipath fading channel, that acquiring and trackinga coherent demodulation reference signal is difficult if not impossible.A noncoherent detector is a detector that does not directly estimate thephase of the received signal. Although differential detection removesthe need for carrier acquisition and tracking in the receiver, itsuffers from a performance penalty (additional required SNR at a givenbit error rate) when compared to ideal (perfect carrier phase reference)coherent detection. The amount of this performance penalty increaseswith the number of phases M and is significant for M≧4. Dariush Divsalarand Marvin K. Simon, in their paper entitled “Multiple-SymbolDifferential Detection of MPSK,” IEEE Transactions on Communications,March 1990 (the disclosure of which is incorporated by reference in itsentirety), presented a differential detection technique involving makinga joint decision on several symbols simultaneously as opposed tosymbol-by-symbol detection. The multiple symbol differential detectiontechnique is a form of maximum-likelihood sequence estimation andassumes that carrier phase is constant during the extended observationinterval, which is typically a reasonable assumption for observations ofthe order of three or four symbol observations. The multiple symboldifferential detector described by Dr. Divsalar and Dr. Simon performshard decisions. A hard decision is a decision between a fixed set ofpossible values (e.g. 0 or 1). In a soft output detector, each bit inthe output also takes on a value indicating reliability.

SUMMARY OF THE INVENTION

Systems and methods for detecting collisions in radio frequency tags inaccordance with embodiments of the invention are disclosed. In oneembodiment, a receiver system includes a receiver configured to receiveand sample a phase modulated input signal, and a multiple symbolnoncoherent soft output detector configured to receive the sampled inputsignal and to generate a soft metric indicative of the reliability of adetected symbol based upon observations over multiple symbols, acollision detector configured to calculate a decision metric from a setof soft metrics generated by the multiple symbol noncoherent soft outputdetector and detect a collision when the decision metric satisfies apredetermined criterion.

In a further embodiment, the soft metric is the Log Likelihood Ratio ofthe detected symbol based upon observations over multiple symbols.

In another embodiment, the observations include observations over a twosymbol sequence.

In a still further embodiment, the observations include observationsover a three symbol sequence.

In still another embodiment, the set of soft metrics generated by themultiple symbol noncoherent soft output detector are generated basedupon observations of a unique sequence of symbols identifying an RFIDtag.

In a yet further embodiment, the unique sequence of symbols identifyingan RFID tag is an RN16 transmission.

In yet another embodiment, the decision metric is based upon a centralmoment of the distribution of the set of soft metrics generated by themultiple symbol noncoherent soft output detector.

In a further embodiment again, the decision metric is normalized over apower of the first moment of the distribution of the set of soft metricsgenerated by the multiple symbol noncoherent soft output detector.

In another embodiment again, the predetermined criterion is the decisionmetric exceeding a threshold.

In a further additional embodiment, the phase modulated input signalincludes a preamble sequence and the threshold is based upon thepreamble correlation normalized by the number of one half symbols usedin the preamble.

In another additional embodiment, the decision metric is a count of thenumber of soft metrics in the set of soft metrics generated by themultiple symbol noncoherent soft output detector.

In a still yet further embodiment, the phase modulated input signalincludes data that is phase modulated on a carrier and the multiplesymbol differential detector assumes that carrier phase of the inputsignal is constant over the time duration of the observations.

In still yet another embodiment, the phase modulated input signal is abinary phase modulated signal.

In a still further embodiment again, the phase modulated input signal isan FM0 modulated signal.

In still another embodiment again, the phase modulated input signal is aMultiple-Phase-Shift Keying modulated signal.

In a still further additional embodiment, the multiple symboldifferential detector includes a plurality of matched filters havingdifferent numbers of samples configured to integrate the samples duringeach half-symbol period, and the multiple symbol differential detectoris configured to use the outputs of each of the plurality of matchedfilters to determine the most likely symbol duration.

Still another additional embodiment also includes an antenna configuredto receive a phase modulated signal that includes symbols transmitted byan RFID tag.

A yet further embodiment again includes receiving and sampling a phasemodulated input signal to produce symbol samples, combining symbolsamples to produce symbol observations, generating a soft metricindicative of the reliability of a detected symbol based upon symbolobservations over multiple symbols, and calculating a decision metricfrom a set of generated soft metrics, and detecting a collision inreceived radio frequency transmissions when the calculated decisionmetric satisfies a predetermined criterion.

In yet another embodiment again, the soft metric is the Log LikelihoodRatio of the detected symbol based upon observations over multiplesymbols.

In a yet further additional embodiment, the observations includeobservations over a two symbol sequence.

In yet another additional embodiment, the observations includeobservations over a three symbol sequence.

In a further additional embodiment again, the set of generated softmetrics were generated based upon observations of a unique sequence ofsymbols identifying an RFID tag.

In another additional embodiment again, the unique sequence of symbolsidentifying an RFID tag is an RN16 transmission.

In a still yet further embodiment again, the decision metric is basedupon a central moment of the distribution of the set of generated softmetrics.

In still yet another embodiment again, the decision metric is normalizedover a power of the first moment of the distribution of the set ofgenerated soft metrics.

In a still yet further additional embodiment, the predeterminedcriterion is the decision metric exceeding a threshold.

In still yet another additional embodiment, the phase modulated inputsignal includes a preamble sequence and the threshold is based upon thepreamble correlation normalized by the number of one half symbols usedin the preamble.

In a yet further additional embodiment again, the decision metric is acount of the number of soft metrics in the set of generated soft metricsthat are below a second threshold.

In yet another additional embodiment again, the phase modulated inputsignal includes data that is phase modulated on a carrier, and themultiple symbol differential detector assumes that carrier phase of theinput signal is constant over the time duration of the observations.

In a still yet further additional embodiment again, the phase modulatedinput signal is a binary phase modulated signal.

In still yet another additional embodiment again, the phase modulatedinput signal is an FM0 modulated signal.

In another further embodiment, the phase modulated input signal is aMultiple-Phase-Shift Keying modulated signal.

In still another further embodiment, combining symbol samples to producesymbol observations also includes using a plurality of matched filtershaving different numbers of samples to integrate the symbol samplesduring each half-symbol period and determining the most likely symbolduration using the integrated symbol samples.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 conceptually illustrates a communication system in accordancewith an embodiment of the invention.

FIGS. 2A-2E illustrate the characteristics of FM0 modulated signalstransmitted in accordance with the EPC Class 1 Generation 2 UHF AirInterface Protocol Standard.

FIG. 3 illustrates the manner in which a hard decision FM0 3-bitmultiple symbol noncoherent soft output detector can be modified togenerate soft metrics.

FIGS. 4A and 4B illustrate sample functions of LLRs over a sequence of16 symbols for the cases of no collision and a two tag collision.

FIG. 5 conceptually illustrates an RFID receiver system that that canperform collision detection in accordance with embodiments of theinvention.

FIGS. 6A and 6B are histograms illustrating LLR simulations for thecases of no collision and a two tag collision using LLRs over threesymbol sequences.

FIGS. 7A and 7B are histograms illustrating simulations of the varianceVar for the cases of no collision and two tag collision using LLRs overthree symbol sequences.

FIGS. 8A and 8B are charts illustrating the simulated probability offalse detection and the probability of miss detection for the cases ofno collision and a two tag collision using LLR over three symbolsequences and the variance of LLR as a decision metric for the cases.

FIGS. 9A-9D are normalized histograms illustrating simulations using theDM2 metric for two cases of no collision and two tag collision withvarious SNR.

FIGS. 10A-10E are normalized histograms of illustrating simulationsusing the DM8 metric for two cases of no collision and two tag collisionwith various SNR.

FIGS. 11A-11C are histograms illustrating LLR simulations for the casesof no collision and two tag collision using LLRs over two symbolsequences.

FIGS. 12A-12D are histograms illustrating simulations of the varianceVar for the cases of no collision and two tag collision using LLRs overtwo symbol sequences.

FIGS. 13A and 13B are charts illustrating the simulated probability offalse detection and the probability of miss detection for the cases ofno collision and a two tag collision using LLR over two symbol sequencesand the variance of LLR as a decision metric.

DETAILED DESCRIPTION

Turning now to the drawings, multiple symbol noncoherent soft outputdetectors that generate soft metrics indicating the reliability ofdetected data in accordance with embodiments of the invention areillustrated. In many embodiments, the multiple symbol noncoherent softoutput detector determines soft metrics based on the log likelihoodratio (LLR) for each detected symbol using observations with respect tomultiple symbols. For received sequences including pilot, preamble, anddata symbols, where the pilot and preamble are known to the detector,the observations utilized to determine the soft metrics for each symbolcan include observations of some or all of the symbols in the pilotand/or preamble and a short sequence of multiple data symbols. Inseveral embodiments, a short sequence of two or three unknown datasymbols is utilized when generating the soft metric for an unknown datasymbol. In other embodiments, a sequence of any number of symbols can beutilized to determine the soft metrics.

The ability of multiple symbol noncoherent soft output detectors inaccordance with embodiments of the invention to produce soft metricsenables the output of more than one receiver to be utilized in thedetection of a transmitted data sequence. In a number of embodiments,soft metrics generated by a set of multiple symbol noncoherent softoutput detectors can be combined to improve the reliability of thedetected data sequence. In several embodiments, the soft metrics can beused to discard the output of one or more multiple symbol noncoherentsoft output detectors in a set of multiple symbol noncoherent softoutput detectors when detecting data. In addition, the soft metrics canbe utilized to select the most reliable output as the detected datasequence. Multiple symbol noncoherent soft output detectors and the useof LLRs when performing multiple symbol noncoherent detection inaccordance with embodiments of the invention are discussed furtherbelow. In order to illustrate multiple symbol noncoherent detectiontechniques in accordance with embodiments of the invention, examples areprovided with respect to the FM0 modulation technique used in commonRadio Frequency Identification (RFID) applications. However, multiplesymbol noncoherent soft output detectors in accordance with embodimentsof the invention can be utilized in any of a variety of applicationsincluding applications involving Multiple Phase Shift Keying, and/orwireless, wired, optical communication channels and systems with channelcoding.

Communication Systems Including Multiple Symbol Noncoherent Soft OutputDetectors

One or more multiple symbol noncoherent soft output detectors inaccordance with embodiments of the invention can be utilized to detectdata in almost any communication system that modulates the phase of thetransmitted signal to communicate information and where the phase of thecarrier signal on which the data is modulated remains relativelyconstant during the transmission of the data sequence. A communicationsystem including a set of multiple symbol noncoherent soft outputdetectors in accordance with embodiments of the invention is illustratedin FIG. 1. The communication system 10 includes a transmitter 12 thatmodulates data symbols onto a carrier for transmission via acommunication channel to one or more receiver systems 14. In theillustrated embodiment, a set of receiver systems 14 is provided andeach receiver system includes a receiver 16 and a multiple symbolnoncoherent soft output detector 18. The receivers 16 demodulate andsample the received signal. The samples are provided to thecorresponding multiple symbol noncoherent soft output detector 18, whichoutputs soft metrics based upon the observations (i.e. the samples).

In several embodiments, the soft metrics based on the LLR are in factthe LLR of each symbol. In a number of embodiments, the soft metricsbased on the LLR are approximations of the magnitude or square of themagnitude of the LLR. In other embodiments, any soft metric thatprovides information concerning the reliability of the detected symbolcan be utilized. The soft metrics can be utilized to detect a receiveddata sequence. In combined receiver systems where only one receiversystem is present, the soft metrics output by the multiple symbolnoncoherent soft output detector can be utilized to generate thereceived data sequence. In the illustrated embodiment, the soft metricsoutput by the multiple symbol noncoherent soft output detectors 18 areprovided to a combiner 20. In a number of embodiments, the combiner 20selects as the detected output a symbol or sequence of symbols basedupon the output of the multiple symbol noncoherent soft output detector18 that detects the symbol or sequence of symbols with the highestreliability. In several embodiments, combiner 20 combines the softmetrics from two or more of the multiple symbol noncoherent soft outputdetectors to generate the detected data sequence. The soft metricsutilized to generate the detected data sequence can be selected basedupon reliability. Alternatively, the combiner 20 can simply combine thesoft metrics of all of the multiple symbol noncoherent soft outputdetectors without regard to the reliability of any specific output.

Although the communication system shown in FIG. 1 shows the use of anantenna 20 to transmit the signal via free space, multiple symbolnoncoherent soft output detectors in accordance with embodiments of theinvention can be utilized in a variety of communication system including(but not limited to) wireless, wired, optical communication systems andsystems with channel coding. An application of particular interest formultiple symbol noncoherent soft output detectors in accordance withembodiments of the invention is the detection of FM0 modulated datatransmitted by Radio Frequency Identification (RFID) tags such as (butnot limited to) Ultra High Frequency RFID tags that conform with the EPCClass 1 Generation 2 UHF Air Interface Protocol (EPC Gen 2) Standardspecified by GS1 AISBL of Brussels, Belgium. Accordingly, much of thediscussion that follows is in the context of detecting FM0 modulatedsignals. However, multiple symbol noncoherent soft output detectors inaccordance with embodiments of the invention can generate soft metricswith respect to symbols generated using a variety of phase modulationtechniques including (but not limited to) Multiple-Phase-Shift Keying(MPSK). If there is no known data available (e.g. no known pilot, orpreamble) the modulation scheme used to transmit the data shouldinherently include differential encoding or a differential encodershould be used. However, if some known data is available a modulationscheme that does not include differential encoding can be used. Systemsand methods for generating soft metrics in accordance with embodimentsof the invention are discussed further below.

Generating Soft Metrics Using Multiple Symbol Noncoherent Soft OutputDetection

Multiple symbol noncoherent soft output detectors in accordance withembodiments of the invention detect received symbols by generating softmetrics using observations of multiple symbols. In several embodiments,the multiple symbol noncoherent soft output detector generates softmetrics based on the LLR of each detected symbol. In order to illustratethe manner in which soft metrics based on LLRs can be utilized in thedetection of a sequence of symbols, the following example is providedwith respect to the detection of FM0 modulated symbols generated inaccordance with the EPC Gen 2 standard. As is discussed further below,each data packet transmitted in accordance with the EPC Gen 2 standardincludes a known pilot and preamble, which can be utilized by thereceiver to improve the reliability of the detected data. Similartechniques can be utilized in communication systems that utilize otherphase modulation techniques and/or for which the receiver system knows aportion of the transmitted sequence.

LLRs for FM0 Symbol Stream Including Pilot and Preamble Sequences

The FM0 basis functions are illustrated in FIG. 2A. A state diagramillustrating the manner in which FM0 modulated symbols are generated isillustrated in FIG. 2B. As can readily be appreciated from the statediagram, each FM0 symbol that is transmitted depends on the previoussymbol. FM0 symbols transmitted depending upon the value of the previoussymbol are illustrated in FIG. 2C. Two bit (two symbol) FM0 sequencesare illustrated in FIG. 2D. The EPC Gen 2 standard specifies that a RFIDtag can transmit FM0 modulated data preceded by a preamble. Theinterrogator can also request that the RFID tag initiate thetransmission with a pilot sequence of 12 leading FM0 zeros. The pilotand preamble sequence of a packet transmitted in accordance with the EPCGen 2 Standard is illustrated in FIG. 2E. Both the pilot and preambleare known to the receiver system. The detection of FM0 modulated datautilizing observations of the pilot and preamble in the generation ofsoft metrics is discussed further below. Increasing the number ofobservations using the pilot and preamble typically improves thereliability of the detected data sequence. Use of observations of knownsymbols is not, however, necessary to detect data using a multiplesymbol noncoherent soft output detector in accordance with embodimentsof the invention.

Consider the FM0 signaling where a data d_(k)ε{±1} generates datax_(k,1)ε{±1} and x_(k,2)ε{±1} such that x_(k,2)=d_(k)x_(k−1,2) andx_(k,1)=−x_(k−1,2).

Let p_(k,i)ε{±1}; k=1, . . . N_(p); i=1,2 represent the pilot andpreamble samples which are known to the receiver. Let x_(k,i)ε{±1}; k=1,. . . N_(d); i=1,2 represent the data. The index i=1 represents thefirst half symbol, and i=2 represents the second half symbol for eachtime index k. Let y_(k,i); k=1, . . . N_(p) and r_(k,i); k=1, . . .N_(d); i=1,2 represent the corresponding noisy complex received samplesafter half-symbol integrations (half symbol matched filtering). As isdiscussed further below, due to timing uncertainty, a number of matchedfilters having different numbers of samples can be utilized to integratethe samples during each half-symbol period to determine the most likelysymbol duration. In the case of FM0, the integration typically commenceshalfway through the symbol interval. The carrier phase φ (uniformlydistributed between 0 and 2π) can be assumed to be almost constant overtime duration of pilot, preamble, and data during reception of a packet.Let I_(m,n) represent a set of time indices k and i corresponding to areceived data observation interval. In particular the assumption can bemade that this set starts with k=m−1, i=2 and ends with k=m+n, i=1. Theconditional probability is

$\begin{matrix}{{{P\left( {\left. r \middle| p \right.,x,\varphi} \right)} = {c_{1}{\mathbb{e}}^{\frac{A}{\sigma^{2}}{{Re}{({{\sum_{k,i}{y_{k,i}p_{k,i}{\mathbb{e}}^{{- j}\;\varphi}}} + {\sum_{k,{i \in I_{m,n}}}{r_{k,i}x_{k,i}{\mathbb{e}}^{{- j}\;\varphi}}}})}}}}}\;} & (1)\end{matrix}$

where c₁ is a constant which depends only on observations. Theexpectation with respect to carrier phase φ is

$\begin{matrix}{{P\left( {\left. r \middle| p \right.,x} \right)} = {{E\left\{ {P\left( {\left. r \middle| p \right.,x,\varphi} \right)} \right\}} = {c_{1}{I_{0}\left( {\frac{A}{\sigma^{2}}{\begin{matrix}{{\left( \sum\limits_{k,i} \right)y_{k,i}p_{k,i}} +} \\{\sum\limits_{k,{i \in I_{m,n}}}{r_{k,i}x_{k,i}}}\end{matrix}}} \right)}}}} & (2)\end{matrix}$Note that Σ_(k,iεI) _(m,n) r_(k,i)x_(k,i)=Σ_(k=m)^(m+n)(r_(k−1,2)−r_(k,1))x_(k−1,2)

The LLR then can be computed as

$\begin{matrix}{\lambda_{k} = {{\ln\;\frac{P\left( {{x_{k} = \left. {+ 1} \middle| p \right.},r} \right)}{P\left( {{x_{k} = \left. {- 1} \middle| p \right.},r} \right)}} = {\ln\;\frac{\sum\limits_{{x:x_{k}} = {+ 1}}{P\left( {\left. x \middle| p \right.,r} \right)}}{\sum\limits_{{x:x_{k}} = {- 1}}{P\left( {\left. x \middle| p \right.,r} \right)}}}}} & (3)\end{matrix}$

For independent identically distributed data, the followingapproximation applies

$\begin{matrix}{\lambda_{k} = {{\ln\frac{\sum\limits_{{x:x_{k}} = {+ 1}}{P\left( {\left. r \middle| p \right.,x} \right)}}{\sum\limits_{{x:x_{k}} = {- 1}}{P\left( {\left. r \middle| p \right.,x} \right)}}}\overset{\sim}{=}\frac{\max_{{x:x_{k}} = {+ 1}}{P\left( {\left. r \middle| p \right.,x} \right)}}{\max_{{x:x_{k}} = {- 1}}{P\left( {\left. r \middle| p \right.,x} \right)}}}} & (4)\end{matrix}$orλ_(k)≅max_(x:x) _(k) ₌₊₁ ln P(r|p,x)−max_(x:x) _(k) ⁼⁻¹ ln P(r|p,x)  (5)

Using ln {I₀(x)}≅x, then for some jε{m, . . . , m+n} the LLR can beobtained as

$\begin{matrix}{\lambda_{j}\overset{\sim}{=}{\frac{A}{\sigma^{2}}\left\{ {{\max\limits_{{x:x_{j}} = {+ 1}}{{{\sum\limits_{k,i}{y_{k,i}p_{k,i}}} + {\sum\limits_{k = m}^{m + n}{\left( {r_{{k - 1},2} - r_{k,1}} \right)x_{{k - 1},2}}}}}} - {\max\limits_{{x:x_{j}} = {- 1}}{{{\sum\limits_{k,i}{y_{k,i}p_{k,i}}} + {\sum\limits_{k = m}^{m + n}{\left( {r_{{k - 1},2} - r_{k,1}} \right)x_{{k - 1},2}}}}}}} \right\}}} & (6)\end{matrix}$

Although the above formulation assumes that the phase modulation takesone of two values, a multiple symbol noncoherent soft output detectorcan be constructed in accordance with embodiments of the invention thatgenerates a LLR with respect to each possible symbol in an M-ary PSKmodulation scheme. In several embodiments, the soft metric is determinedrelative to the likelihood of an arbitrarily selected reference symbolvalue. Referring back to the case where the phase can take one of twovalues, the generation of LLRs using observations over 3-symbol FM0modulated sequences in accordance with embodiments of the invention isdiscussed below.

LLR for 3-Bit Duration

Assuming that time synchronization is already acquired, the term|Σ_(k,i)y_(k,i)p_(k,i)+Σ_(k=m) ^(m+n)(r_(k−1,2)−r_(k,1))x_(k−1,2)| canbe written for a 3-bit (3 symbol) estimation as

$\begin{matrix}{{{\sum\limits_{k,i}{y_{k,i}p_{k,i}}} + {\left( {r_{{m - 1},2} - r_{m,1}} \right)x_{{m - 1},2}} + {\left( {r_{m,2} - r_{{m + 1},1}} \right)x_{m,2}} + {\left( {r_{{m + 1},2} - r_{{m + 2},1}} \right)x_{{m + 1},2}}}} & (7)\end{matrix}$

Since x_(m,2)=d_(m)x_(m−1,2), x_(m+1,2)=d_(m+1)d_(m)x_(m−1,2) (7) can berewritten asf(x _(m−1,2) ,d _(m) ,d _(m+1) ,t)

$\begin{matrix}{{{\sum\limits_{k,i}{y_{k,i}p_{k,i}}} + {x_{{m - 1},2}\left\lbrack {\left( {r_{{m - 1},2} - r_{m,1}} \right) + {\left( {r_{m,2} - r_{{m + 1},1}} \right)d_{m}} + {\left( {r_{{m + 1},2} - r_{{m + 2},1}} \right)d_{m}d_{m + 1}}} \right\rbrack}}} & (8)\end{matrix}$where t corresponds to timing index.

The detector of an RFID receiver such as the RFID Receiver described inU.S. Pat. No. 7,633,377 entitled “RFID Receiver” to Ramin Sadr (thedisclosure of which is incorporated by reference herein in its entirety)can be replaced with a multiple symbol noncoherent soft output detectorin accordance with an embodiment of the invention. The RFID receiverdescribed in U.S. Pat. No. 7,633,377 provides time synchronization usingthe pilot and preamble symbols to within +/−1 sample. For punctualtiming (no timing error) set t=0, for early timing (by one sampleforward) set t=+1, and for late timing (by one sample backward) sett=−1. This index t namely −1, 0, or +1 corresponds to the starting timeof matched filtering (integrate and dump for FM0 pulses). When timesynchronization is provided with respect to t=−1, 0, and +1, softmetrics for each time index can be obtained as follows using a multiplesymbol noncoherent soft output detector in accordance with embodimentsof the invention.

With these notations then the conditional LLR for time index t forinformation data is

$\begin{matrix}{{\lambda\left( {d_{m},t} \right)} = {\frac{A}{\sigma^{2}}\begin{Bmatrix}{{\max\limits_{x_{{m - 1},2},d_{m + 1}}{f\left( {x_{{m - 1},2},1,d_{m + 1},t} \right)}} -} \\{\max\limits_{x_{{m - 1},2},d_{m + 1}}{f\left( {x_{{m - 1},2},{- 1},d_{m + 1},t} \right)}}\end{Bmatrix}}} & (9)\end{matrix}$

The timing correction can be obtained as{circumflex over (t)}=arg max_(t=−1,0,+1){|λ(d _(m) ,t)|}  (10)then the unconditional LLR for time index {circumflex over (t)} forinformation data is λ (d_(m))

(d_(m), {circumflex over (t)}). As can readily be appreciated, timesynchronization may be less precise and a greater number of conditionalLLRs are calculated in determining the timing correction.

The |Σ_(k,i)y_(k,i)p_(k,i)| can be used as an estimate for amplitude A.The 3-bit (3 symbol) window can then be slid by one bit (symbol)duration and the process repeated to correct timing and obtain the LLRfor the next bit (symbol).

Combining LLRs

LLRs determined using processes similar to those outlined above can becombined at the output of detectors for n receivers asλ(d _(m))=Σ_(i−1) ^(n)λ_(i)(d _(m))  (11)

The final decision on information data d_(m) is{circumflex over (d)} _(m)=sign(λ(d _(m)))  (12)

As noted above, reliability thresholds can be applied to the softmetrics determined by each receiver and soft metrics that indicate lowreliability can be excluded from the final decision. In manyembodiments, the final decision is based on the soft metric or softmetrics that indicate the highest reliability.

Hardware Implementations of 3-bit FM0 Multiple Symbol Noncoherent SoftOutput Detectors

RFID receivers that implement 3-bit multiple symbol detectors thatperform hard decision detection are described in U.S. Pat. No. 7,633,377(incorporated by reference above). In U.S. Pat. No. 7,633,377, themetric shown in FIG. 15 d and equation (41) is formulated based on theproperty of FM0 modulation that x_(m,2)=d_(m)x_(m−1,2),x_(m,1)=−x_(m−1,2) as follows (utilizing the notation presented above)|(r _(m−1,2) −r _(m,1))d _(m)+(r _(m,2) −r _(m+1,1))+(r _(m+1,2) −r_(m+2,1))d _(m+1|)  (13)

When the same metric is formulated based on the property of FM0modulation that x_(m,2)=d_(m)x_(m−1,2), x_(m+1,2)=d_(m+1)d_(m)x_(m−1,2),the following equivalent metric is obtained|(r _(m−1,2) −r _(m,1))+(r _(m,2) −r _(m+1,1))d _(m)+(r _(m+1,2) −r_(m+2,1))d _(m) d _(m+1|)  (14)or equivalentlyg(d _(m) ,d _(m+1))=|(r _(m−1,2) −r _(m,1))+(r _(m,2) −r _(m+1,1))d_(m)+(r _(m+1,2) −r _(m+2,1))d _(m) d _(m+1)|²  (15)

A hard decision can be performed to determine d_(m) as

$\begin{matrix}{{\hat{d}}_{m} = {\arg\;{\max\limits_{d_{m},d_{m + 1}}{g\left( {d_{m},d_{m + 1}} \right)}}}} & (16)\end{matrix}$

When accounting for timing correction, this becomesg(d _(m) ,d _(m+1) ,t)=|[(r _(m−1,2) −r _(m,1))+(r _(m,2) −r _(m+1,1))d_(m)+(r _(m+1,2) −r _(m+2,1))d _(m) d _(m+1)]|²  (17)where t is for timing correction.

A hard decision can be performed to detect d_(m) as

$\begin{matrix}{\hat{d} = {\arg\;{\max\limits_{{t = {- 1}},0,{+ 1}}{\max\limits_{d_{m},d_{m + 1}}{g\left( {d_{m},d_{m + 1},t} \right)}}}}} & (18)\end{matrix}$

However the above g(d_(m), d_(m+1), t) is equivalent tog(d _(m) ,d _(m+1) ,t)=|[(r _(m−1,2) −r _(m,1))d _(m)+(r _(m,2) −r_(m+1,1))+(r _(m+1,2) −r _(m+2,1))d _(m+1)]|²  (19)or from the point of data decision and timing is also equivalent tog(d _(m) ,d _(m+1) ,t)=|(r _(m−1,2) −r _(m,1))+(r _(m,2) −r _(m+1,1))d_(m)+(r _(m+1,2) −r _(m+2,1))d _(m) d _(m+1|)  (20)

Accordingly, a multiple symbol noncoherent soft output detector can beimplemented with minor modification to the detector disclosed U.S. Pat.No. 7,633,377 by using the correlations that were generated prior to thehard decision to generate the soft output as follows:

$\begin{matrix}{{\lambda\left( {d_{m},t} \right)} = {\frac{A}{\sigma^{2}}\begin{Bmatrix}{{\max_{d_{m + 1}}{g^{\prime}\left( {1,d_{m + 1},t} \right)}} -} \\{\max_{d_{m + 1}}{g^{\prime}\left( {{- 1},d_{m + 1},t} \right)}}\end{Bmatrix}}} & (21)\end{matrix}$where g′(d_(m), d_(m+1),t)=|(r_(−1,2)−r_(m,1))+(r_(m,2)−r_(m+1,1))d_(m)+(r_(m+1,2)−r_(m+2,1))d_(m)d_(m+1)|

Alternatively, we can compute

$\begin{matrix}{{\lambda\left( {d_{m + 1},t} \right)} = {\frac{A}{\sigma^{2}}\left\{ {{\max\limits_{d_{m}}{g^{\prime}\left( {d_{m},{+ 1},t} \right)}} - {\max\limits_{d_{m}}{g^{\prime}\left( {d_{m},{- 1},t} \right)}}} \right\}}} & \left( {21a} \right)\end{matrix}$

where the maximum is taken over d_(m)=+1 and d_(m)=−1.

However, an approximation can be used if power computation is easierthan complex absolute value calculation as

$\begin{matrix}{{{\lambda\left( {d_{m},t} \right)} = {\frac{A}{\sigma^{2}}\begin{Bmatrix}{{\max_{d_{m + 1}}{g\left( {1,d_{m + 1},t} \right)}} -} \\{\max_{d_{m + 1}}{g\left( {{- 1},d_{m + 1},t} \right)}}\end{Bmatrix}}}{where}{{g\left( {d_{m},d_{m + 1},t} \right)} = {\begin{matrix}{\left( {r_{{m - 1},2} - r_{m,1}} \right) + {\left( {r_{m,2} - r_{{m + 1},1}} \right)d_{m}} +} \\{\left( {r_{{m + 1},2} - r_{{m + 2},1}} \right)d_{m}d_{m + 1}}\end{matrix}}^{2}}{A = {{\sum\limits_{k,i}{y_{k,i}p_{k,i}}}}}} & (22)\end{matrix}$which comes from preamble synchronization circuits. If complex absolutevalue computation cannot be done, A² can be used as an approximation.

Based upon the above discussion, the hardware implementation of thedetector disclosed in U.S. Pat. No. 7,633,377 can be modified byreplacing the maximum operation in the hardware implementation of thehard detection decision (i.e.

$\max\limits_{d_{m},d_{m + 1}}{{g\left( {d_{m},d_{m + 1},t} \right)}\left. \quad \right)}$with two maximum operation blocks that are subtracted (i.e. max_(d)_(m+1) g(1, d_(m+1), t)−max_(d) _(m+1) g(−1, d_(m+1), t)). Themodification to the detector disclosed in U.S. Pat. No. 7,633,377 toachieve a multiple symbol noncoherent soft output detector in accordancewith embodiments of the invention is illustrated in FIG. 3. The powercomputation g(d_(m), d_(m+1),t) is represented as P_(d) _(m) _(,d)_(m+1) . The maximum value of P_(1,1) and P_(1,−1) is determined using afirst maximum block 42 and the maximum value of P_(−1,1,) and P_(−1,−1)is determined using a second maximum block 44. The two maximums are thensubtracted using a subtraction block 46 to generate a value proportionalto the LLR λ(d_(m),t). The result of the subtraction can be weighted byA or A² to produce a soft metric based on the LLR. Obtaining softmetrics using the above hardware implementation does not alter thetiming correction scheme utilized by the hardware detector.

For symbol stream combining, the timing of the soft metrics from two ormore receivers should be aligned. In instances where the receivers arein close vicinity of each other and data rates are low, such additionaltiming alignment is not as important. When combining soft outputs frommultiple receivers, the noise variances for identical RF front ends fortwo or more receivers with the same Noise Figure (NF) are almost thesame. Therefore, σ² need not be calculated for each receiver. If this isnot the case, then for each receiver in addition to received amplitude(or power) computation the received noise variance σ² is calculatedprior to combining.

Although a specific hardware implementation is discussed above basedupon modifying the RFID receiver disclosed in U.S. Pat. No. 7,633,377,any of a variety of receiver designs can be utilized to implementmultiple symbol noncoherent soft output detectors that produce softoutputs in accordance with embodiments of the invention. Additionalfunctionality including (but not limited to) collision detection thatcan be supported by a receiver configured to produce soft metrics inaccordance with embodiments of the invention are discussed furtherbelow.

Collision Detection

The soft metrics generated by a multiple symbol noncoherent soft outputdetector in accordance with an embodiment of the invention can beutilized to perform collision detection. When a population of RFID tagsresponds to a transmission, such as an interrogation signal, a collisioncan occur when a receiver system receives responses from multiple tags.

Sample functions of LLRs over a sequence of 16 symbols when there is nocollision and when there is a two tag collision are illustrated in FIGS.4A and 4B. In FIG. 4A, sample functions of 16 LLRs with a very high SNRare shown. As can be seen in the figure, in the case of no collisionrepresented by curve 160, the LLRs are at nearly a constant value. Inthe case of a two tag collision represented by curve 162, some LLRs arenearly double the value of the LLRs in curve 160 (resulting from symbolsbeing summed) and some LLRs are nearly zero (resulting from symbolscancelling out). In FIG. 4B, sample functions of 16 LLRs with a SNR of 8dB are shown. As a result of interference and/or noise, the LLRs havemore diverse values than in the case of high SNR in FIG. 4A. In the caseof no collision represented by curve 166, the LLRs are close to a meanvalue. In the case of a two tag collision represented by curve 168, theLLRs have more divergent values (resulting from symbols being summed andcancelling out).

In many embodiments of the invention, an RFID receiver system that canbe used for collision detection includes a half symbol integrator,multiple symbol noncoherent detector, and collision detector. An RFIDreceiver system that performs collision detection in accordance withembodiments of the invention is illustrated in FIG. 5. The receiversystem 50 includes a phased antenna array with antennas 52. Each antenna52 directs a signal to a delay 54 and correlator 56. The delay 54 andcorrelator 56 feed into a phase derotator 58. A combiner 60 receives theoutput of the phase derotators 58 and provides a signal to a half symbolintegrator 62. A difference block 64 calculates the differences at bitboundaries (i.e., between a second one-half symbol and the subsequentfirst one-half symbol) and provides the information to a three bitmultiple symbol noncoherent detector 66. The noncoherent detector 66calculates LLRs from the half-symbol differences and provides theinformation to a collision detector 68. Systems and methods fordetecting collisions utilizing LLRs are discussed below.

Referring again to the example of FM0 modulated data transmitted by RFIDtags in accordance with the EPC Gen 2 standard, RFID collision detectioncan be performed using the soft metrics generated when detecting an RFIDtag's RN16 query response. The RN16 query response is a 16 bit randomnumber that is assigned to each tag. As is discussed further below, acollision during the transmission of the RN16 bits can be detected usingthe soft metrics based on LLRs of the bits detected by a multiple symbolnoncoherent soft output detector in accordance with embodiments of theinvention. LRRs can be computed from short sequences of symbols withinthe RN16 transmission (e.g. two or three symbols).

Assuming that the preamble is already detected, the LLR based onobserved 3-bit (symbol) duration utilized for performing collisiondetection is as follows:

$\begin{matrix}{\lambda_{i} = {{\max\limits_{d}{{\left( {r_{{i - 1},2} - r_{i,1}} \right) + \left( {r_{i,2} - r_{{i + 1},1}} \right) + {\left( {r_{{i + 1},2} - r_{{i + 2},1}} \right)d}}}} - {\max\limits_{d}{{\left( {r_{{i - 1},2} - r_{i,1}} \right) - \left( {r_{i,2} - r_{{i + 1},1}} \right) - {\left( {r_{{i + 1},2} - r_{{i + 2},1}} \right)d}}}}}} & (23)\end{matrix}$

This LLR can be computed for i=1, 2, 3, . . . , 15 and d=+1 and −1(where the maximum is taken over d=+1 and d=−1). For simplicity

$\frac{A}{\sigma^{2}}$is dropped in (23). On the edges of RN16, r_(0,2) is known from the lastone-half symbol observation from the preamble sequence. For r_(17,1) ifit is not available we can set r_(17,1)=−r_(16,2). The method is basedon observing |λ_(i)| for i=1, 2, 3, . . . , 15.

Note that we can also compute λ_(i+1) based on the same observations as:

$\begin{matrix}{\lambda_{i + 1} = {\max\limits_{d}{{{\begin{matrix}{\left( {r_{{i - 1},2} - r_{i,1}} \right) + {\left( {r_{i,2} - r_{{i + 1},1}} \right)d} +} \\{\left( {r_{{i + 1},2} - r_{{i + 2},1}} \right)d}\end{matrix}{{- \underset{d}{\quad\max}}}\left( {r_{{i - 1},2} - r_{i,1}} \right)} + {\left( {r_{i,2} - r_{{i + 1},1}} \right)d} - {\left( {r_{{i + 1},2} - r_{{i + 2},1}} \right)d}}}}} & \left( {23a} \right)\end{matrix}$

In particular this can be used (for i=15) to compute λ₁₆ (for the lastbit in RN16) if it is desired. However, for collision detection we useLLR for 15 bits but one can also use 16 bits. If such as follows we needonly to do averaging over 16 bits rather 15 and use magnitude of 16LLRs.

When there is no collision the one-half symbol observations are:r _(i,j) =A ₁ x _(i,j) e ^(jφ) ¹ +n _(i,j)  (24)

For i=0, 1, 2, . . . , 16 and j=1, 2.

When there is a two tag collision the one-half symbol observations are:r _(i,j) =A ₁ x _(i,j) e ^(jφ) ¹ +A ₂ x′ _(i,j) e ^(jφ) ² +n_(i,j)  (25)

For i=0, 1, 2, . . . , 16 and j=1, 2. All phases are unknown anduniformly distributed. As discussed further above, one-half symbols canbe obtained at the output of a one-half symbol integrator by summing thenumber of samples per one-half symbol taken with a matched filter andcorrecting for timing as in equation (10).

One method to discriminate collision versus no collision is to usevariance of LLR over the 15-bit (symbol) received RN16 transmission as adecision metric. The variance can be defined as:

$\begin{matrix}{{Var} = {{\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}^{2}}} - \left( {\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}}} \right)^{2}}} & (26)\end{matrix}$

The variance can be compared to a threshold to detect collisions. Inseveral embodiments, a threshold TH=m|corr| is utilized, where “corr”represents the result of preamble correlation normalized by the numberof one half symbols used in the preamble, and m is a number that can beset based on a desired false detection probability appropriate to aspecific application. Based on the above, the magnitude of “corr” can beexpressed as

$\begin{matrix}{{{corr}} = {\frac{1}{2N_{p}}{{\sum\limits_{k,i}{y_{k,i}p_{k,i}}}}}} & (27)\end{matrix}$

If Var>TH then a collision is declared.

A histogram of LLR simulations for two cases of no collision and two tagcollision where the received SNR of each tag is the same is illustratedin FIG. 6A. The histogram 100 illustrates a curve 102 of the probabilitythat the magnitude of an LLR is a certain value plotted against possiblevalues for the magnitude of an LLR when there is no collision and theRFID tag has a Signal to Noise Ratio (SNR) of 12 dB. A curve 104 showsthe probability that the magnitude of an LLR is a certain value plottedagainst possible values for the magnitude of an LLR when there is a twotag collision where each tag has a SNR of 12 dB. As can be seen in thechart, the curve 102 for no collision lies mostly between 5 and 20 andpeaks sharply near a mean value. Meanwhile, the curve 104 for collisiondrops from a high sharply between 0 and 5 and remains low from 5 to 30.

Similarly, a histogram of LLR simulations for two cases of no collisionand a two tag collision where the received SNR of the first tag is 12 dBand the received SNR of the second tag is 9 dB is illustrated in FIG.6B. Similar to FIG. 6A, the curve 122 for no collision lies mostlybetween 5 and 20 and peaks sharply near a mean value. The curve 124 forcollision has a smaller peak near 5 and remains low from 10 to 25. Fromthe stark differences in the shape of these curves for the case ofcollision versus the case of no collision, it can be seen that thevariance as computed in equation (26) and other techniques fordescribing the shape of a distribution that are discussed further below(e.g., using central moment about the mean) can be used to distinguishesbetween the two cases. For example, variance measures the spread of adistribution. In FIGS. 6A and 6B it can be seen that the curves in thecase of no collision are more narrow than the curves in the case ofcollision, and therefore the variance will be smaller. Using variance asin equation (26) and a threshold TH=m|corr| using equation (27), an mcan be chosen to give a threshold TH that can distinguish between thevariance of a curve where there is no collision and the variance of acurve where there is a collision.

Histograms of the variance Var for the cases of no collision and two tagcollision are illustrated in FIGS. 7A and 7B. In FIG. 7A one tag has anSNR of 12 dB while the other tag has an SNR of 9 dB. In FIG. 7B the twotags each have an SNR of 12 dB. As can be seen in the figures, thecurves for the case of no collision (125 in FIGS. 7A and 127 in FIG. 7B)concentrate and peak around different values from the curves for thecase of a collision (126 in FIGS. 7A and 128 in FIG. 7B). Particularlywhere the SNR is higher (9 and 12 dB) there is very little overlap inthe curves of Var. Accordingly, a threshold TH can be determined usingthe equations described above for effectively distinguishing betweencollision and no collision.

A simulation of the probability of a false detection and the probabilityof a miss detection using LLR as in equation (23) the variance of LLR asin equation (26) as a decision metric when the colliding tags have thesame SNR is illustrated in FIG. 8A. As can be seen from the chart 130,both the probability of false detection 132 and the probability of missdetection decrease with increased SNR. The probability of falsedetection 132 trails off considerably relative to the probability ofmiss detection 134 with increased SNR due to the effectiveness of thethreshold in identifying two tag collisions. Therefore, the probabilityof miss detection does not diminish as steeply with increased SNR. FIG.8B is a similar chart to FIG. 8A with the exception that the simulationinvolves a two tag collision, where the SNR of the signal received fromthe first tag is 3 dB greater than the signal received from the secondtag. As can be seen from the chart 140, the probability of falsedetection 142 and the probability of miss detection 144 exhibit similarcharacteristics even when the signal of one tag dominates. Accordingly,the simulations indicate that the stronger the received signal the morelikely that the LLR magnitude output by the multiple symbol noncoherentsoft output detector can be utilized to accurately detect collisions.

Other methods of collision detection involve using the mean (firstmoment) of the magnitude of LLR over the 15-bit (symbol) received RN16transmission. One example is taking the ratio of the second moment ofLLR over the 15-bit received RN16 over the square of the first moment ofLLR over the 15-bit received RN16. This decision metric DM2 can bedefined as:

$\begin{matrix}{{{DM}\; 2} = {\left( {\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}^{2}}} \right)/\left( {\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}}} \right)^{2}}} & (28)\end{matrix}$

Normalizing in this way helps to keep the threshold constant over a widerange of signal to noise ratios. The metric DM2 can be compared to athreshold that is set to a number. In the case of no collision, themetric DM2 is nearly one for a range of signal to noise ratios in whichRFID receivers operate. In the case of a collision, the metric DM2 isstrictly greater than one.

Further methods of collision detection can use the ratio of highermoments of LLR over the 15-bit received RN over powers of the firstmoment of LLR over the 15-bit received RN16. One further method utilizesthe normalized m-th central moment of the LLRs as a decision metric DMmas follows:

$\begin{matrix}{{DMm} = {\frac{\frac{1}{15}{\sum\limits_{i = 1}^{15}\left( {{\lambda_{i}} - {\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}}}} \right)^{m}}}{\left( {\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}}} \right)^{m}} + {constant}}} & (29)\end{matrix}$

For example the decision metric DM4 using the fourth central moment canbe defined as:

$\begin{matrix}{{{DM}\; 4} = {\frac{\frac{1}{15}{\sum\limits_{i = 1}^{15}\left( {{\lambda_{i}} - {\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}}}} \right)^{4}}}{\left( {\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}}} \right)^{4}} + {constant}}} & (30)\end{matrix}$

The metric DM4 can be compared to a threshold that is set to a number.The constant can be set to any number that simplifies the selection ofthe threshold. In the case of no collision, the metric DM4 is almost aconstant number (the constant). In the case of collision, the metric DM4will be strictly greater than the constant. For example, if the constantis 3, then the metric DM4 will be close to 3 when there is no collisionand will be strictly greater than 3 when there is a collision.

Normalized histograms of simulations using the DM2 metric for two casesof no collision and two tag collision with various SNR are illustratedin FIGS. 9A-9D. In each chart, the plot of col shows cases where thereis a two tag collision and the plot of no col shows cases where there isno collision. In FIG. 9A the two RFID tags each have an SNR of 20 dB, inFIG. 9B the two tags each have an SNR of 15 dB, in FIG. 9C the two tagseach have an SNR of 10, and in FIG. 9D one tag has an SNR of 15 and theother tag has an SNR of 10. As can be seen in the charts, DM2 typicallyremains very close to 1 in the case of no collisions for various SNR andcan vary from close to 1 to close to 4 in the case of collisions.Furthermore, there is almost no overlap between the histogram of DM2when there is no collision and the histogram of DM2 when there is a twotag collision. Accordingly, the simulations indicate that one way todetermine a threshold for the DM2 metric is to use experimentation orobservation to choose a threshold to distinguish between the twosituations of collision versus no collision.

Using equation 29, a decision metric DM8 can be formed by using m=8.Normalized histograms of simulations using the DM8 metric for two casesof no collision and two tag collision with various SNR are illustratedin FIGS. 10A-E. In each chart, the plot of col shows cases where thereis a two tag collision and the plot of no col shows cases where there isno collision. In FIG. 10A one tag has an SNR of 20 and the other tag hasan SNR of 15, in FIG. 10B one tag has an SNR of 15 and the other tag hasan SNR of 10, in FIG. 10C one tag has an SNR of 10 and the other tag hasan SNR of 5, in FIG. 10D the two tags each have an SNR of 20, and inFIG. 10E the two tags each have an SNR of 5. Similar to the histogramsillustrated above in FIGS. 9A-9D, DM8 typically remains very close to 1in the case of no collisions for various SNR and can vary quite far from1 in the case of collisions. Particularly, if the difference in SNRbetween two tags is less than 5 dB, a threshold for DM8 can be used veryeffectively to distinguish between collision and no collision.

Yet another method to detect collisions involves the observation that,in the case of a collision, the magnitude of a number of LLRs will bevery low. Each |λ_(i)| for i=1, 2, . . . , 15 can be compared with athreshold. In several embodiments, a threshold can be set based on

$\frac{1}{15}{\sum\limits_{i = 1}^{15}{\lambda_{i}}}$or its normalized version. A count is taken for the number of times that|λ_(i)| for i=1, 2, . . . , 15 is below the threshold. The count,referred to as an m-count, can be used as a decision metric by comparingit to an integer count threshold. In many embodiments, the countthreshold is between 2 and 8 inclusive. A collision can be declared ifthe m-count is greater than the count threshold.

Next, consider a 2-bit (symbol) duration time. Assuming that thepreamble is already detected, the LLR based on observed 2-bit (symbol)duration utilized for performing collision detection is as follows:λ_(i)|(r _(i−1,2) −r _(i,1))+(r _(i,2) −r _(i+1,1))|−|(r _(i−1,2) −r_(i,1))−(r _(i,2) −r _(i+1,1))|  (31)

This LLR can be computed for i=1, 2, 3, . . . , 15, 16. For simplicity

$\frac{A}{\sigma^{2}}$is dropped in (28). On the edges of RN16, r_(0,2) is known from the lastone-half symbol observation from the preamble sequence. For r_(17,1) ifit is not available we can set r_(17,1)=−r_(16,2). The method is basedon observing |λ_(i)| for i=1, 2, . . . , 16.

When there is no collision:r _(i,j) =A ₁ x _(i,j) e ^(jφ) ¹ +n _(i,j)  (32)

For i=0, 1, 2, . . . , 16 and j=1, 2.

When there is a two tag collision the one-half symbol observations are:r _(i,j) =A ₁ x _(i,j) e ^(jφ) ¹ +A ₂ x′ _(i,j) e ^(jφ) ² +n_(i,j)  (33)

For i=0, 1, 2, . . . , 16 and j=1, 2. All phases are unknown anduniformly distributed. As discussed further above, one-half symbols canbe obtained at the output of a one-half symbol integrator by summing thenumber of samples per one-half symbol taken with a matched filter andcorrecting for timing as in equation (10).

One method to discriminate collision versus no collision is to useKullback-Leibler divergence. For two density functions P and Q theKullback-Leibler divergence is defined as:

$\begin{matrix}{D\left( {{P\left. Q \right)} = {\sum\limits_{i}{{P(i)}\log\;\frac{P(i)}{Q(i)}}}} \right.} & (34)\end{matrix}$

Another method is to use variance of LLR over the 16-bit (symbol)received RN16 transmission as a decision metric. The variance can bedefined as:

$\begin{matrix}{{Var} = {{\frac{1}{16}{\sum\limits_{i = 1}^{16}{\lambda_{i}}^{2}}} - \left( {\frac{1}{16}{\sum\limits_{i = 1}^{16}{\lambda_{i}}}} \right)^{2}}} & (35)\end{matrix}$

The variance can be compared to a threshold to detect collisions. Inseveral embodiments of the invention, a threshold TH=m|corr| isutilized, where “corr” represents the result of preamble correlationnormalized by the number of one half symbols used in the preamble, and mis a number that can be set based on a desired false detectionprobability appropriate to a specific application. Based on the above,the magnitude of “corr” can be expressed as:

$\begin{matrix}{{{corr}} = {\frac{1}{2N_{p}}{{\sum\limits_{k,i}{y_{k,i}p_{k,i}}}}}} & (36)\end{matrix}$

If Var>TH then a collision is declared.

A histogram of LLR simulations for two cases of no collision and two tagcollision where the received SNR of each tag is the same is illustratedin FIG. 11A. The histogram 160 illustrates a curve 162 of theprobability that the magnitude of an LLR is a certain value plottedagainst possible values for the magnitude of an LLR when there is nocollision and the RFID tag has a Signal to Noise Ratio (SNR) of 6 dB. Acurve 164 shows the probability that the magnitude of an LLR is acertain value plotted against possible values for the magnitude of anLLR when there is a two tag collision where each tag has a SNR of 6 dB.As can be seen in the chart, the curve 162 for no collision lies mostlybetween 0 and 10 and peaks sharply near a mean value. Meanwhile, thecurve 164 for collision drops from a high sharply between 0 and 5 andremains low from 5 to 10.

Similarly, a histogram of LLR simulations for two cases of no collisionand a two tag collision where the received SNR of each tag is 12 dB isillustrated in FIG. 11B. Similar to FIG. 11A, the curve 172 for nocollision lies mostly between 7 and 18 and peaks sharply near a meanvalue. The curve 174 for collision drops from a high sharply between 0and 5 and remains low from 5 to 30. A histogram of LLR simulations wherethe received SNR of one tag is 12 dB and the other tag is 9 dB isillustrated in FIG. 11C. Similarly again, the curve 182 for no collisionlies mostly between 0 and 18 and peaks sharply near a mean value. Thecurve 184 for collision has a smaller peak near 5 and remains low from10 to 30.

From the stark differences in the shape of these curves for the case ofcollision versus the case of no collision, it can be seen that thevariance as computed in equation (35) and other techniques fordescribing the shape of a distribution that are discussed further above(e.g., using central moment about the mean) can be used to distinguishesbetween the two cases. For example, variance measures the spread of adistribution. In FIGS. 6A and 6B it can be seen that the curves in thecase of no collision are narrower than the curves in the case ofcollision, and therefore the variance will be smaller. Using variance asin equation (35) and a threshold TH=m|corr| using equation (36), an mcan be chosen to give a threshold TH that can distinguish between thevariance of a curve where there is no collision and the variance of acurve where there is a collision.

Histograms of the variance Var for the cases of no collision and two tagcollision are illustrated in FIGS. 12A-12D. In FIG. 12A the two tagshave an SNR of 6 dB, in FIG. 12B the two tags have an SNR of 12 dB, inFIG. 12C one tag has an SNR of 6 dB while the other tag has an SNR of 3dB, and in FIG. 12D one tag has an SNR of 12 dB while the other tag hasan SNR of 9 dB. As can be seen in the figures, the curves for the caseof no collision and the case of a collision concentrate and peak arounddifferent values. Particularly where the SNR is higher (9 and 12 dB)there is very little overlap in the curves of Var. Accordingly, athreshold TH can be determined using the equations described above foreffectively distinguishing between collision and no collision.

A simulation of the probability of a false detection and the probabilityof a miss detection using LLR as in equation (31) and the variance ofLLR as in equation (35) as a decision metric when the colliding tagshave the same SNR is illustrated in FIG. 13A. As can be seen from thechart, both the probability of false detection and the probability ofmiss detection decrease with increased SNR, even for differentthresholds TH=m|corr| where m=4 and 6. The probability of falsedetection trails off considerably relative to the probability of missdetection 134 with increased SNR due to the effectiveness of thethreshold in identifying two tag collisions. As can be seen in thecharts, lowering m in TH=m|corr| reduces both the probably of falsedetection and the probability of miss detection.

FIG. 13B is a similar chart to FIG. 13A with the exception that thesimulation involves a two tag collision where the SNR of the signalreceived from the first tag is 3 dB greater than the signal receivedfrom the second tag. As can be seen from the chart, the probability offalse detection and the probability of miss detection exhibit similarcharacteristics even when the signal of one tag dominates. Accordingly,the simulations indicate that the stronger the received signal the morelikely that the LLR magnitude output by the multiple symbol noncoherentsoft output detector can be utilized to accurately detect collisions.

Although specific procedures for performing collision detection in RFIDsystem using LLR magnitudes are discussed above, any of a variety oftechniques utilizing LLR magnitudes and/or other soft metrics can beutilized to perform collision detection in a variety of applicationsincluding (but not limited to) RFID tag interrogation in accordance withembodiments of the invention.

While the above description contains many specific embodiments of theinvention, these should not be construed as limitations on the scope ofthe invention, but rather as an example of one embodiment thereof.Accordingly, the scope of the invention should be determined not by theembodiments illustrated, but by the appended claims and theirequivalents.

What is claimed is:
 1. A receiver system, comprising: a receiverconfigured to receive and sample a phase modulated input signal; and amultiple symbol noncoherent soft output detector configured to receivethe sampled input signal and to generate a soft metric indicative of thereliability of a detected symbol based upon observations of a uniquesequence of symbols identifying an RFID tag; a collision detectorconfigured to calculate a decision metric from a set of soft metricsgenerated by the multiple symbol noncoherent soft output detector anddetect a collision when the decision metric satisfies a predeterminedcriterion.
 2. The receiver system of claim 1, wherein the soft metric isthe Log Likelihood Ratio of the detected symbol based upon observationsover multiple symbols.
 3. The receiver system of claim 2, wherein theobservations include observations over a two symbol sequence.
 4. Thereceiver system of claim 2, wherein the observations includeobservations over a three symbol sequence.
 5. The receiver system ofclaim 1, wherein the unique sequence of symbols identifying an RFID tagis an RN16 transmission.
 6. The receiver system of claim 1, wherein thedecision metric is based upon a central moment of the distribution ofthe set of soft metrics generated by the multiple symbol noncoherentsoft output detector.
 7. The receiver system of claim 6, wherein thedecision metric is normalized over a power of the first moment of thedistribution of the set of soft metrics generated by the multiple symbolnoncoherent soft output detector.
 8. The receiver system of claim 6,wherein the predetermined criterion is the decision metric exceeding athreshold.
 9. The receiver system of claim 8, wherein the phasemodulated input signal includes a preamble sequence and the threshold isbased upon the preamble correlation normalized by the number of one halfsymbols used in the preamble.
 10. The receiver system of claim 1,wherein the decision metric is a count of the number of soft metrics inthe set of soft metrics generated by the multiple symbol noncoherentsoft output detector.
 11. The receiver system of claim 1, wherein: thephase modulated input signal comprises data that is phase modulated on acarrier; and the multiple symbol differential detector assumes thatcarrier phase of the input signal is constant over the time duration ofthe observations.
 12. The receiver system of claim 11, wherein the phasemodulated input signal is a binary phase modulated signal.
 13. Thereceiver system of claim 11, wherein the phase modulated input signal isan FM0 modulated signal.
 14. The receiver system of claim 11, whereinthe phase modulated input signal is a Multiple-Phase-Shift Keyingmodulated signal.
 15. The receiver system of claim 1, wherein: themultiple symbol differential detector comprises a plurality of matchedfilters having different numbers of samples configured to integrate thesamples during each half-symbol period; and the multiple symboldifferential detector is configured to use the outputs of each of theplurality of matched filters to determine the most likely symbolduration.
 16. The receiver system of claim 1, further comprising anantenna configured to receive a phase modulated signal comprisingsymbols transmitted by an RFID tag.
 17. A method for detectingcollisions in received radio frequency transmissions, the methodcomprising: receiving and sampling a phase modulated input signal toproduce symbol samples; combining symbol samples to produce symbolobservations; generating a soft metric indicative of the reliability ofa detected symbol based upon symbol observations of a unique sequence ofsymbols identifying an RFID tag; calculating a decision metric from aset of generated soft metrics; and detecting a collision in receivedradio frequency transmissions when the calculated decision metricsatisfies a predetermined criterion.
 18. The method of claim 17, whereinthe soft metric is the Log Likelihood Ratio of the detected symbol basedupon observations over multiple symbols.
 19. The method of claim 18,wherein the observations include observations over a two symbolsequence.
 20. The method of claim 18, wherein the observations includeobservations over a three symbol sequence.
 21. The method of claim 17,wherein the unique sequence of symbols identifying an RFID tag is anRN16 transmission.
 22. The method of claim 17, wherein the decisionmetric is based upon a central moment of the distribution of the set ofgenerated soft metrics.
 23. The method of claim 22, wherein the decisionmetric is normalized over a power of the first moment of thedistribution of the set of generated soft metrics.
 24. The method ofclaim 22, wherein the predetermined criterion is the decision metricexceeding a threshold.
 25. The method of claim 24, wherein the phasemodulated input signal includes a preamble sequence and the threshold isbased upon the preamble correlation normalized by the number of one halfsymbols used in the preamble.
 26. The method of claim 17, wherein thedecision metric is a count of the number of soft metrics in the set ofgenerated soft metrics that are below a second threshold.
 27. The methodof claim 17, wherein: the phase modulated input signal comprises datathat is phase modulated on a carrier; and the multiple symboldifferential detector assumes that carrier phase of the input signal isconstant over the time duration of the observations.
 28. The method ofclaim 27, wherein the phase modulated input signal is a binary phasemodulated signal.
 29. The method of claim 27, wherein the phasemodulated input signal is an FM0 modulated signal.
 30. The method ofclaim 27, wherein the phase modulated input signal is aMultiple-Phase-Shift Keying modulated signal.
 31. The method of claim18, wherein combining symbol samples to produce symbol observationsfurther comprises: using a plurality of matched filters having differentnumbers of samples to integrate the symbol samples during eachhalf-symbol period; and determining the most likely symbol durationusing the integrated symbol samples.